def rdft_lu_solver(a,b,r=[]): (fra, fr) = rdft(a,r) frb = fr.dot(b) (l,u) = lu.lu(fra) y = lu.l_step(l,frb) x = lu.u_step(u,y) return x
def rdft_lu_solver(a, b, r=[]):
(fra, fr) = rdft(a, r)
frb = fr.dot(b)
(l, u) = lu.lu(fra)
y = lu.l_step(l, frb)
x = lu.u_step(u, y)
return x
def rdft_lu_solver_with_lu(a,b,r=[]): (fra, fr) = rdft(a,r) frb = fr.dot(b) fra_save = np.array(fra) frb_save = np.array(frb) (l,u) = lu.lu(fra) y = lu.l_step(l,frb) x = lu.u_step(u,y) return (x, l, u, fra_save, frb_save, fr)
def rdft_lu_solver_with_lu(a, b, r=[]):
(fra, fr) = rdft(a, r)
frb = fr.dot(b)
fra_save = np.array(fra)
frb_save = np.array(frb)
(l, u) = lu.lu(fra)
y = lu.l_step(l, frb)
x = lu.u_step(u, y)
return (x, l, u, fra_save, frb_save, fr)
def solve_gauss(a, b, x):
(size, _) = a.shape
g = rdft.generate_g(size)
ga = g.dot(a)
ga_save = np.array(ga)
gb = g.dot(b)
(l, u) = lu.lu(ga)
y = lu.l_step(l, gb)
x1 = lu.u_step(u, y)
x2 = np.array(x1)
x2 = iteration.iteration_another(a, l, u, g, b, x2, linalg.cond(ga))
return (x2, ga, a, x1)
def solve_gauss(a,b,x): (size,_) = a.shape g = rdft.generate_g(size) ga = g.dot(a) ga_save = np.array(ga) gb = g.dot(b) (l,u) = lu.lu(ga) y = lu.l_step(l,gb) x1 = lu.u_step(u,y) x2 = np.array(x1) x2 = iteration.iteration_another(a, l, u, g, b, x2, linalg.cond(ga)) return (x2, ga, a, x1)
def iteration_step_result(a, l, u, b, x, a_cond):
(size,_) = a.shape
itera, itermax = 0, 1
a_nrm = linalg.norm(a, float("inf"))
x_nrm = linalg.norm(x, float("inf"))
x_step_result = [x]
cte = math.log10(a_cond) * math.sqrt(size)/10
r = b - a.dot(x)
r_nrm = linalg.norm(r, float("inf"))
while itera < min(cte, itermax):
y = lu.l_step(l, r)
z = lu.u_step(u, y)
x = x + z
x_step_result.append(x)
r = b - a.dot(x)
x_nrm = linalg.norm(x, float("inf"))
r_nrm = linalg.norm(r, float("inf"))
itera = itera + 1
return x_step_result
def solve_rdft_givens_both(a,b,x): (size,_) = a.shape f = rdft.generate_f(size) r = rdft.generate_r(size) g1 = givens.givens_generation(size) g2 = givens.givens_generation(size) fr = f.dot(r) frg = fr.dot(g1) frgb = frg.dot(b) ag = a.dot(g2) frgag = frg.dot(ag) (l,u) = lu.lu(frgag) y = lu.l_step(l,frgb) z = lu.u_step(u,y) x1 = g2.dot(z) x2 = np.array(x1) x2 = iteration.iteration_another(a, l, u, frg, b, x2, linalg.cond(frgag), g2) x2 = iteration.remove_imag(x2) return (x2, x1)
def iteration_another(a, l, u, fr, b, x, a_cond, rm=[]):
(size,_) = a.shape
itera, itermax = 0, 1
a_nrm = linalg.norm(a, float("inf"))
x_nrm = linalg.norm(x, float("inf"))
#cte = math.log10(a_cond) * math.sqrt(size)/10
r = fr.dot(b - a.dot(x))
r_nrm = linalg.norm(r, float("inf"))
while itera < itermax:
y = lu.l_step(l, r)
z = lu.u_step(u, y)
if rm == []:
x = x + z
else:
x = x + rm.dot(z)
r = fr.dot(b - a.dot(x))
x_nrm = linalg.norm(x, float("inf"))
r_nrm = linalg.norm(r, float("inf"))
itera = itera + 1
return x
def solve_rdft_givens_both(a, b, x):
(size, _) = a.shape
f = rdft.generate_f(size)
r = rdft.generate_r(size)
g1 = givens.givens_generation(size)
g2 = givens.givens_generation(size)
fr = f.dot(r)
frg = fr.dot(g1)
frgb = frg.dot(b)
ag = a.dot(g2)
frgag = frg.dot(ag)
(l, u) = lu.lu(frgag)
y = lu.l_step(l, frgb)
z = lu.u_step(u, y)
x1 = g2.dot(z)
x2 = np.array(x1)
x2 = iteration.iteration_another(a, l, u, frg, b, x2, linalg.cond(frgag),
g2)
x2 = iteration.remove_imag(x2)
return (x2, x1)
def lu_solver(a,b): (l,u,c) = plu(a,b) y = lu.l_step(l,c) x = lu.u_step(u,y) return x